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Abstract <p>Hypergraphic automata are automata, state sets and output symbol sets of which are hypergraphs, being invariant under actions of transition and output functions. Universally attracting objects in the category of such automata are called universal hypergraphic automata. Their semigroups of input symbols are algebras of mappings for such automata. Therefore, their properties are interconnected with the properties of the algebraic structures of universal hypergraphic automata. This paper describes the structure of monomorphisms of these automata and their semigroups of input symbols. The main result is a solution to this problem for universal hypergraphic automata over effective hypergraphs with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p\)</EquationSource> <!--LobJMat2561410Khvorostukhina-m1--> </InlineEquation>-definable edges. This is a wide and very important class of automata because such algebraic systems contain automata whose state hypergraphs and hypergraphs of output symbols are projective or affine planes.</p>

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On Monomorphisms of Universal Hypergraphic Automata

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • E. V. Khvorostukhina

摘要

Abstract

Hypergraphic automata are automata, state sets and output symbol sets of which are hypergraphs, being invariant under actions of transition and output functions. Universally attracting objects in the category of such automata are called universal hypergraphic automata. Their semigroups of input symbols are algebras of mappings for such automata. Therefore, their properties are interconnected with the properties of the algebraic structures of universal hypergraphic automata. This paper describes the structure of monomorphisms of these automata and their semigroups of input symbols. The main result is a solution to this problem for universal hypergraphic automata over effective hypergraphs with \(p\) -definable edges. This is a wide and very important class of automata because such algebraic systems contain automata whose state hypergraphs and hypergraphs of output symbols are projective or affine planes.